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A comment of the combinatorics of the vertex operator Γ_(t|X)
release_dhnahbee5zfldfphrxvsdrvfea
by
Mercedes Helena Rosas
Released
as a article
.
2017
Abstract
The Jacobi--Trudi identity associates a symmetric function to any integer
sequence. Let Γ_(t|X) be the vertex operator defined by
Γ_(t|X) s_α =∑_n ∈Z s_(n,α) [X] t^n. We
provide a combinatorial proof for the identity Γ_(t|X) s_α =
σ[tX] s_α[x-1/t] due to Thibon et al. We include an
overview of all the combinatorial ideas behind this beautiful identity,
including a combinatorial description for the expansion of s_(n,α) [X]
in the Schur basis, for any integer value of n.
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1701.02516v2
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